Manning-type potential induced by kink scatterings with phonons in molecular chains with hyperbolic double-well substrates

TL;DR

This paper derives a rescaled Manning potential from kink scattering in a molecular chain model, accounting for isotope effects and substrate variations, applicable to diverse molecular and quantum systems.

Contribution

It introduces a generalized hyperbolic substrate potential with a tunable parameter, enabling modeling of molecular excitations across various systems with inversion symmetry.

Findings

Derived a rescaled Manning potential from kink scattering analysis.

Showed the model's applicability to diverse molecular systems.

Highlighted the influence of substrate parameter variations on molecular excitations.

Abstract

A rescaled Manning potential is obtained in the analysis of scatterings of small- amplitude excitations with a kink defect. The generic model is a nonlinear Klein- Gordon Hamiltonian describing a one-dimensional chain of identical molecules, sub- jected to an hyperbolic single-particle substrate potential. To account for isotope effects that are likely to affect characteristic equilibrium parameters of the molec- ular chain, including the lattice spacing (i.e. the characteristic intermolecuar dis- tance) and/or the barrier height, the hyperbolic substrate potential is endowed with a real parameter whose variation makes it suitable for the description of molecu- lar excitations in a broad range of systems with inversion symmetry. These include hydrogen-bonded molecular crystals, {\alpha}-helix proteins, long polymer chains and two- state quantum-tunneling systems in general. Double-well models with deformable profiles are relevant in physical contexts where the equilibrium configurations are sensitive to atomic or molecular substitutions, dilution, solvation and so on.